On the stability of kalman-bucy diffusion processes

Publication Type:
Journal Article
SIAM Journal on Control and Optimization, 2017, 55 (6), pp. 4015 - 4047
Issue Date:
Full metadata record
Files in This Item:
Filename Description Size
16m1102707.pdfPublished Version330.6 kB
Adobe PDF
© 2017 Society for Industrial and Applied Mathematics. The Kalman-Bucy filter is the optimal state estimator for an Ornstein-Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the Bayes filter for continuous state-space models. Consequently, this filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy. The purpose of this work is to review, re-prove and refine existing results concerning the dynamical properties of the Kalman-Bucy filter so far as they pertain to filter stability and convergence. The associated differential matrix Riccati equation is a focal point of this study with a number of bounds, convergence, and eigenvalue inequalities rigorously proven. New results are also given in the form of exponential and comparison inequalities for both the filter and the Riccati ow.
Please use this identifier to cite or link to this item: